Geometric realisation as the Skorokhod semi-continuous path space endofunctor
Algebraic Topology
2020-09-24 v1 General Topology
Abstract
We interpret a construction of geometric realisation by [Besser], [Grayson], and [Drinfeld] of a simplicial set as constructing a space of maps from the interval to a simplicial set, in a certain formal sense, reminiscent of the Skorokhod space of semi-continuous functions; in particular, we show the geometric realisation functor factors through an endofunctor of a certain category. Our interpretation clarifies the explanation of [Drinfeld] "why geometric realization commutes with Cartesian products and why the geometric realization of a simplicial set [...] is equipped with an action of the group of orientation preserving homeomorphisms of the segment [0,1]".
Keywords
Cite
@article{arxiv.2009.11030,
title = {Geometric realisation as the Skorokhod semi-continuous path space endofunctor},
author = {Misha Gavrilovich and Konstantin Pimenov},
journal= {arXiv preprint arXiv:2009.11030},
year = {2020}
}